Question

A sample of gas weighs 10.1 g and occupies a volume of 5.65 l at 60 °c and 580 torr. Identify the gas sample.

Answer 1

The question is incomplete, here is the complete question:

A sample of gas weighs 10.1 g and occupies a volume of 5.65 L at 60 °C and 580 torr. Identify the gas sample.

(a) $CHCl_3$ (molar mass = 119.4 g/mol)  

(b) $N_2O$ (molar mass = 44.02 g/mol)

(c) $SO_2$ (molar mass = 64.07 g/mol)

(d) $NH_3$ (molar mass = 17.03 g/mol)

(e) $Cl_2$ (molar mass = 70.90 g/mol)

Answer: The gas sample is $SO_2$ having molar mass of 64 g/mol

Explanation:

To calculate the molar mass of the gas, we use the equation given by ideal gas equation:

PV = nRT

Or,

$PV=\frac{w}{M}RT$

where,

P = Pressure of the gas = 580 torr

V = Volume of the gas = 5.65 L

w = Weight of the gas = 10.1 g

M = Molar mass of gas = ?

R = Gas constant = $62.36\text{ L. Torr }mol^{-1}K^{-1}$

T = Temperature of the gas = $60^oC=[60+273]K=333K$

Putting values in above equation, we get:

$580torr\times 5.65L=\frac{10.1g}{M}\times 62.364\text{ L. torr }mol^{-1}K^{-1}\times 333K\\\\M=\frac{10.1\times 62.364\times 333}{580\times 5.65}=64g/mol$

Hence, the gas sample is $SO_2$ having molar mass of 64 g/mol